Joint subgrid velocity-scalar filtered mass density function method for compressible turbulent flows

Abstract

In large eddy simulations (LESs) and scalar filtered mass density functions, a gradient diffusion model is generally used for subgrid-scale (SGS) scalar flux modeling. However, this hypothesis is known to generate evident errors under certain conditions, particularly when the counter-gradient scalar transport effect dominates. Herein, a joint subgrid velocity-scalar filtered mass density function (VSGSSFMDF) method is developed to address this problem. The exact FMDF transport equation is derived in detail. Based on the order of the magnitude analysis and simply Langevin model, the FMDF transport equation is modeled, and a system of stochastic differential equations is, thus, proposed. Theoretical derivation and analysis suggest that both the first- and second-order moments are consistent. A compressible mixing layer and hydrogen/air-reactive mixing layer are simulated to verify the proposed method. Based on the diffusion model, a direct numerical simulation and an LES are performed for comparative verification. A generally reasonable SGS velocity distribution is obtained using the proposed VSGSSFMDF method. Consequently, the counter-gradient scalar transport effect is effectively simulated using this method. Overall, the VSGSSFMDF produces better results than the SFMDF and LES in both cases, particularly in the reactive case.